Exact $S$-duality Map for Rigid Surface Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917135405547520 |
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| author | Li, Chuanzhong Luo, Xiaoman Shou, Bao |
| author_facet | Li, Chuanzhong Luo, Xiaoman Shou, Bao |
| contents | Surface operators in four-dimensional gauge theories are two-dimensional defects, serving as natural generalizations of Wilson lines and 't Hooft line operators. They act as ideal probes for exploring the non-perturbative structure of the theory. Rigid surface operators are a specific class of surface operators characterized by the absence of continuous deformation parameters. It is expected that a closed $S$-duality map should exist among these rigid operators. While progress has been made on specific examples or subclasses by leveraging invariants and empirical conjectures, a complete picture remains elusive.
A significant challenge arises when multiple rigid surface operators share identical invariants, making the determination of $S$-duality relations difficult. More critically, a mismatch exists in the number of rigid surface operators between dual theories when classified by invariants; this is referred to as the \textit{mismatch problem}. This discrepancy suggests the necessity of extending the scope of consideration beyond strictly rigid operators.
In this paper, we propose a direct, natural, and precise $S$-duality map for rigid surface operators.
Our map is realized by moving the longest row in the pair of partitions defining a surface operator from one factor to the other, with an additional box appended or deleted to balance the total number of boxes.
This mapping naturally incorporates non-rigid surface operators, thereby resolving the mismatch problem. The proposed map is applicable to gauge groups of all ranks and clarifies several long-standing puzzles in the field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact $S$-duality Map for Rigid Surface Operators Li, Chuanzhong Luo, Xiaoman Shou, Bao High Energy Physics - Theory Surface operators in four-dimensional gauge theories are two-dimensional defects, serving as natural generalizations of Wilson lines and 't Hooft line operators. They act as ideal probes for exploring the non-perturbative structure of the theory. Rigid surface operators are a specific class of surface operators characterized by the absence of continuous deformation parameters. It is expected that a closed $S$-duality map should exist among these rigid operators. While progress has been made on specific examples or subclasses by leveraging invariants and empirical conjectures, a complete picture remains elusive. A significant challenge arises when multiple rigid surface operators share identical invariants, making the determination of $S$-duality relations difficult. More critically, a mismatch exists in the number of rigid surface operators between dual theories when classified by invariants; this is referred to as the \textit{mismatch problem}. This discrepancy suggests the necessity of extending the scope of consideration beyond strictly rigid operators. In this paper, we propose a direct, natural, and precise $S$-duality map for rigid surface operators. Our map is realized by moving the longest row in the pair of partitions defining a surface operator from one factor to the other, with an additional box appended or deleted to balance the total number of boxes. This mapping naturally incorporates non-rigid surface operators, thereby resolving the mismatch problem. The proposed map is applicable to gauge groups of all ranks and clarifies several long-standing puzzles in the field. |
| title | Exact $S$-duality Map for Rigid Surface Operators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.08801 |